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Energy in nuclear reactions

  1. Aug 16, 2013 #1
    Hello forum.

    So the other day I was pondering properties of atomic nucleus, in particular the property of binding energy (mass defect). Whenever a nucleus -- through a nuclear reaction of some sort -- is split or joined into a more stable nucleus, energy is released. However the newly formed nucleus which is more stable has more binding energy than the nucleus from which it formed. How can we then say that energy is released? Is it not rather contradictory? The binding energy grew post-reaction, but should it not have decreased since energy was released?

    (Maybe I am just interpreting binding energy incorrectly, since it essentially just measures the change in mass in nucleons in a free versus bounded state and therefore does not necessarily have anything to do with the pre-reaction nucleus).

    If we look at masses-per-nucleon, this problem can be intuitively explained: The newly formed and more stable nucleus has less mass-per-nucleon than the nucleus from which it formed. According to E = mc^2, that means that the new nucleus cumulatively has less energy than the pre-reaction nucleus in terms of the masses of the elementary particles. Thus one realizes the nucleons lost energy during the reaction and one can reasonably conclude that lost energy was the energy released in the reaction.

    Another perspective on the same problem is that "less stable" can be interpreted as "more/highly energized". So if a nucleus joins/splits into a more stable one, we can conclude that this "excess" (if you will) energy prior to the reaction has been released throughout the reaction. So this is why for example iron will not spontaneously join/split into any other nucleus. It is because iron is as stable is at gets (for all intents and purposes) and in order for iron to form a less-stable nucleus (i.e. more energized nucleus), energy must be inserted externally into the system.

    Much appreciated if anyone could help me understand how the increasing of binding energy despite releasing energy throughout the reaction is true.
  2. jcsd
  3. Aug 16, 2013 #2


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    Binding energy is always negative (you need energy to split the atoms into protons and neutrons), and "more binding energy" / "larger binding energy" ... always means "more negative" (more energy is needed to separate them).

    Edit: Clarified
    Last edited: Aug 16, 2013
  4. Aug 16, 2013 #3
    What, really? I have never heard of that, care to elaborate? Also, what are your thoughts on the other two explanations I presented?
  5. Aug 16, 2013 #4


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    Per wiki:

    Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than the sum of its constituent parts — this is what keeps the system together. Often this means that energy is released upon the creation of a bound state. This definition corresponds to a positive binding energy. (This definition also often causes confusion. For example: A prominent term in chemistry is the 'free energy of binding', which is the difference between the bound and unbound states and thus negative).

    And your explanations are more or less correct. A higher binding energy per nucleon means that it takes MORE energy per nucleon to disassemble the nucleus.
  6. Aug 16, 2013 #5


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    Suppose you have a boulder sitting on top of a cliff. If you give the boulder a little nudge, it will fall off the cliff. When it hits the ground, it releases energy (heat, sound, etc). It is now more stable, because giving it a nudge can't cause it to fall any further, it's at the bottom and has nowhere else to go. The boulder at the bottom of the cliff is also now more tightly bound to the earth. If you wanted to launch the boulder out of earth's gravitational influence, it would take more energy to do so starting from the bottom of the cliff than the top.
  7. Aug 25, 2013 #6
    Excellent responses, I believe I have finally grasped it intuitively. Thanks!
  8. Aug 27, 2013 #7


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    Question: Is binding energy measured in Joules/Mole? I'm having wikipedia issues...
  9. Aug 27, 2013 #8


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    It is possible to express binding energy in Joule/Mole, but that is a very unconventional unit for nuclear physics. MeV/atom or MeV/nucleon are more common.
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